15.7.2 Limit theorems

Problem: Let \( \xi_{1}, \xi_{2}, \ldots \) is the sequence of such independent non-negative random variables that \( p\left(\xi_{n}>c\right)=0 \). Prove that the series \( \sum \xi_{n} \) almost surely converges only when the series \( \sum E \xi_{n} \) converges.